Teaching

A collection of my recitation problems and handwritten lecture notes for Penn’s Math 114 (multivariable calculus) are hosted at Professor Robert Ghrist’s site, here.

A few additional worked problems and solutions

• Vol. 1 Ch.1-6 | Solutions
• Vol. 1 Ch.7-12 | Solutions
• Vol. 1 Ch.10-15 | Solutions
• Vol. 1 Ch.13-18 | Solutions
• Vol. 1 Ch.16-18 ; Vol. 2 Ch.1-3 | Solutions

Other Potentially Useful Material for the course

Volume 1

• T,N,B Frame Acceleration Equation Derived
• T,N,B Frame Example
• Parametrizing the Intersection of Two Planes
• Dot Product Formula Derived
• Row Reduction Example

Volume 2

• Inverse Function Theorem Example
• Implicit Function Theorem Example
• The Gradient is Perpendiciular to Level Sets: Somewhat of a Proof
• Tangent Plane Intuition
• Tangent Planes and Gradients (Example)
• Linearization (Example)
• Hessian: Determinant and Trace Intuition

Volume 3

• Lagrange Multiplier Example
• Changing Integration Order (1)
• Changing Integration Order (2)
• Changing Integration Order (3)
• Center of Mass Example
• Inertia Matrix and Rotation about a Skew Axis
• Change of Variables Intuition

Volume 4

• Green’s Theorem Intuition
• Scalar Path Integral Intuition
• Some Intuition on 1-Forms
• Path Independence/Dependence
• Integrating 2-Forms Example